You have been watching videos of Chopin's music? One does not really need 4k to get quality video. Good technique and sensible equipment will do the job. 1080p is absolutely fine. You also need to consider if your viewer has 4k screens, or a suitable internet speed to view streaming 4k. Also consider if you record in 4k, you have to deal with 4k file sizes and workflow. I put together a stage plot on what looks to be going on. Cam 1: DSLR, telephoto, user operated during performance (Viewable at 1:16)Cam 2: ENG camera?, wide angle (See the Busoni vid)Cam 3: Camcorder, wide, remote operated / zoom in postCam 4: Action cam, wide, zoom in post, placed very near or inside rim of pianoOn a single stand:Rec 1: Lower on stand, Tascam DR-100 or similarRec 2: Higher on stand, Zoom H4n or similarIMO, Cam 1 is very likely a 5DMkII, there are clues in the photographers Flickr stream.There is a huge difference between 1080p on a phone and 1080p on a full frame camera, and that is sensor size. It is that sensor size which is a major factor in the impression of greater quality. Better dynamic range, contrast, color rendition, sharpness, plus the headroom to edit and adjust in post. If you are shooting on a small sensor phone and the output is already noisy, there is not much room to be adjusting exposure in post before you get a mess of unflattering grain and artifacts. On a decent camcorder, and of course DSLR / mirrorless, you can adjust for white balance. You know when colors look all wonky and white surfaces turn blue, or skin tones appear orange. It is usually a matter of calibrating the white balance for the ambient light sources. It takes a few seconds and will save you from headaches in post. A lot of people blame it on the camera, but the user has the responsibility to set the calibration. It is a simple thing that can make a video look "right." In the present video, you can see there was a bit of a color temperature clash by a cool light source, but the videographer adjusted for the predominant ambient sources, so it all looks balanced (1:54 - see the reflections of the cool light source on the piano and on her hair). Lenses. DSLR / mirrorless give you the option to changes lenses. Yes they can get expensive, but you can get some quality vintage film lenses cheap and make good videos. Autofocus lenses are not a requirement for video lenses, especially things like filming recitals. Depth of field. In the 0:35 closeup shot, see how there are portions of the frame that are in-focus and the foreground and background elements are out of focus. It looks polished, draws your eyes into a specific part of the frame, and generally stands out compared to cell phone shot video. Depth of field is a big topic, but at the risk of oversimplifying: a camera with access to large aperture and sensor will make this effect more pronounced. Do you need expensive gear to do this? No - a 50mm f/1.8 on an APS-C sensor will still have narrower depth of field than a typical phone. The multi-camera approach does add a sense of finish to the video. It allows the viewer to experience various angles as well as focal lengths. This video is done well, and it is easy to focus on the music and performer. Some film makers get too overzealous with cine effects and make impressive looking videos that are distracting to watch for a music focused listener. I think the opening focus change (out of focus to in focus shot) was done in post, not in camera. As for fps, keep in mind as you raise your fps, you also raise the minimum shutter speed. Raising your shutter speed means you get less light to the sensor. Using the exposure triangle, you would calculate proper exposure by adjusting ISO and aperture. So there is a give and take. Generally ideal shutter speed for natural movement is the reciprocal of 2x the fps. So for 30 fps, your ideal shutter is 1/60. Phone cameras were mentioned a lot above. I'm not knocking phone cameras, just a lot of people will be able to relate to one. Good stuff can be done on consumer gear with the right techniques.
I would think youtube is standardizing or doing something to the videos if they're all at 30fps. I remember something about the pitch being slightly off on their videos but that was many years ago now.